Real-time measurement of ventricular stroke volume variations by continuous arterial pulse contour analysis

ABSTRACT

Ventricular stroke volume variation (SVV) is estimated as a function of the standard deviation of arterial blood pressure value measured over each of at least two cardiac cycles, preferably over each of the cardiac cycles in a computation interval covering a full respiratory cycle. In one embodiment, maximum and minimum standard deviation values are determined over the computation interval. SVV is then estimated proportional to the ratio of the difference between the maximum and minimum standard deviation values and the mean of the standard deviation values. In another embodiment, SVV is then estimated proportional to the ratio of the standard deviation of the standard deviation values and the mean standard deviation over the entire computation interval. A pre-processing arrangement for improving reliability of estimates of more general cardiac or hemodynamic parameters is also disclosed and involves smoothing with an approximating function, and sampling and low-pass filtering at an adjustable rate.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of and incorporates by reference U.S.patent application Ser. No. 11/085,957 filed on Mar. 22, 2005 which is acontinuation-in-part of, claims priority of, and incorporates byreference co-pending U.S. patent application Ser. Nos. 10/728,705 filed5 Dec. 2003 now issued as U.S. Pat. No. 7,220,230, and Ser. No.10/890,887, filed 14 Jul. 2004.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates in general to cardiac monitoring and inparticular to estimation of ventricular stroke volume variation (SVV) aswell as to a system that implements the method.

2. Background Art

Stroke volume (SV), cardiac output (CO), etc., are important indicatorsnot only for diagnosis of disease, but also for “real-time” monitoringof the condition of both human and animal subjects, including patients.Few hospitals are therefore without some form of equipment to monitorone or more of these cardiac parameters. Many techniques—invasive andnon-invasive, as well as those that combine both—are in use and evenmore have been proposed in the literature.

Most of the techniques used to measure SV can usually be readily adaptedto provide an estimate of CO as well, since CO is generally defined asSV times the heart rate HR, which is usually available to monitoringequipment. Conversely, most devices that estimate CO also estimate SV asa sub-step.

As is explained in greater detail below, still another cardiac parameterthat promises to provide clinically important information is strokevolume variation SVV. One way to estimate SVV is simply to collectmultiple SV values and calculate the differences from measurementinterval to measurement interval.

One common way to measure SV or CO is to mount some flow-measuringdevice on a catheter, and then to thread the catheter into the subjectand to maneuver it so that the device is in or near the subject's heart.Some such devices inject either a bolus of material or energy (usuallyheat) at an upstream position, such as in the right atrium, anddetermine flow based on the characteristics of the injected material orenergy at a downstream position, such as in the pulmonary artery,Patents that disclose implementations of such invasive techniques (inparticular, thermodilution) include:

U.S. Pat. No. 4,236,527 (Newbower et al., 2 Dec. 1980);

U.S. Pat. No. 4,507,974 (Yelderman, 2 Apr. 1985);

U.S. Pat. No. 5,146,414 (McKown, et al., 8 Sep. 1992); and

U.S. Pat. No. 5,687,733 (McKown, et al., 18 Nov. 1997).

Still other invasive devices are based on the known Fick technique,according to which CO is calculated as a function of oxygenation ofarterial and mixed venous blood.

Invasive techniques have obvious disadvantages, the main one of which isof course that catheterization of the heart is potentially dangerous,especially considering that the subjects (especially intensive carepatients) on which it is performed are often already in the hospitalbecause of some actually or potentially serious condition. Invasivemethods also have less obvious disadvantages: Some techniques such asthermodilution rely on assumptions, such as uniform dispersion of theinjected heat, that affect the accuracy of the measurements depending onhow well they are fulfilled. Moreover, the very introduction of aninstrument into the blood flow may affect the value (for example, flowrate) that the instrument measures.

Doppler techniques, using invasive as well as non-invasive transducers,are also used to measure flow and to calculate SV and CO from the flowmeasurements. Not only are these systems typically expensive, but theiraccuracy depends on precise knowledge of the diameter and generalgeometry of the flow channel. Such precise knowledge is, however, seldompossible, especially under conditions where real-time monitoring isdesired.

There has therefore been a long-standing need for some way ofdetermining cardiac parameters such as SV, SVV, etc., that is bothnon-invasive, or at most minimally invasive, and accurate. One bloodcharacteristic that has proven particularly promising for accuratelydetermining such parameters with minimal or no invasion is bloodpressure.

Most known blood-pressure-based systems rely on the so-called pulsecontour method (PCM), which calculates an estimate of the cardiacparameter(s) of interest from characteristics of the beat-to-beatpressure waveform. In the PCM, “Windkessel” (German for “air chamber”)parameters (characteristic impedance of the aorta, compliance, and totalperipheral resistance) are typically used to construct a linear ornon-linear, hemodynamic model of the aorta. In essence, blood flow isanalogized to a flow of electrical current in a circuit in which animpedance is in series with a parallel-connected resistance andcapacitance (compliance). The three required parameters of the model areusually determined either empirically, through a complex calibrationprocess, or from compiled “anthropometric” data, that is, data about theage, sex, height, weight, etc., of other patients or test subjects. U.S.Pat. No. 5,400,793 (Wesseling, 28 Mar. 1995) and U.S. Pat. No. 5,535,753(Petrucelli, et al., 16 Jul. 1996) are representative of systems thatrely on a Windkessel circuit model to determine CO.

PCM-based systems can monitor SV-derived cardiac parameters more or lesscontinuously, with no need for a catheter (usually right heart) to beleft in the patient. Indeed, some PCM systems operate using bloodpressure measurements taken using a finger cuff. One drawback of PCM,however, is that it is no more accurate than the rather simple,three-parameter model from which it is derived; in general, a model of amuch higher order would be needed to faithfully account for otherphenomena, such as the complex pattern of pressure wave reflections dueto multiple impedance mis-matches caused by, for example, arterialbranching. Because the accuracy of the basic model is usually not goodenough, many improvements have been proposed, with varying degrees ofcomplexity

The “Method and apparatus for measuring cardiac output” disclosed bySalvatore Romano in U.S. Published Patent Application 20020022785 A1 (21Feb. 2002, “Method and apparatus for measuring cardiac output”)represents a different attempt to improve upon PCM techniques byestimating SV, either invasively or non-invasively, as a function of theratio between the area under the entire pressure curve and a linearcombination of various components of impedance. In attempting to accountfor pressure reflections, the Romano system relies not only on accurateestimates of inherently noisy derivatives of the pressure function, butalso on a series of empirically determined, numerical adjustments to amean pressure value.

Fluid administration in hemodynamically unstable patients is often amajor challenge when it comes to measuring SV, CO, or other hemodynamicparameters in real time. Correct clinical assessment of hypovolemia isdifficult, as is the decision to undertake fluid resuscitation as theinitial treatment strategy. Specifically, it is very difficult topredict whether a hemodynamically unstable patient will respond to fluidtherapy with an increase in stroke volume and cardiac output. Moreover,fluid overload can cause significant pulmonary or cardiac dysfunction,whereas fluid insufficiency may cause tissue damage resulting in vitalorgan dysfunction. A patient's fluid responsiveness is the major andmost important determinant to assess the adequacy of fluid resuscitationtherapy and to ensure optimal cardiac performance and organ perfusion.

Many bedside indicators of ventricular preload have been used aspredictors of fluid responsiveness. Right arterial pressure (RAP) andpulmonary artery occlusion pressure (PAOP) are the most commonly used inthe intensive care unit (ICU) when deciding to administer fluids. Otherbedside indicators of ventricular preload include right ventricular enddiastolic volume (RVEDV) and left ventricular end diastolic area (LVEDA)measured with transesophageal echocardiography. Several studies and casereports have shown, however, that these static indicators based oncardiac filling pressures have poor predictive value and often fail togive adequate information about fluid responsiveness.

Recently, several studies have confirmed the clinical significance ofmonitoring the variations observed in left ventricular stroke volumethat result from the interaction of the cardiovascular system and thelungs under mechanical ventilation. These stroke volume variations (SVV)are caused by the cyclic increases and decreases in the intrathoracicpressure due to the mechanical ventilation, which lead to variations inthe cardiac preload and afterload. SVV has recently been extensivelyinvestigated and several studies have shown the usefulness of using SVVas predictor of fluid responsiveness in various clinical situations.Several other parameters based on SVV have been found to be useful aswell. In particular, systolic pressure variation (SPV) with its delta-Up(ΔUp) and delta-Down (ΔDown) components has been found to be a veryuseful predictor of fluid responsiveness. SPV is based on the changes inthe arterial pulse pressure due to respiration-induced variations instroke volume. Yet another parameter that has recently been investigatedand shown to be a valid indicator of fluid responsiveness is the pulsepressure variation (PPV).

Recent developments in arterial pulse contour analysis methods haveopened unique opportunities for less-invasive, continuous and real-timeestimation of SVV. This allows clinicians to use SVV routinely alongwith SV and CO in their assessment of the hemodynamic state of criticalcare patients.

Existing systems for measuring fluid responsiveness based onrespiration-induced changes in the arterial pulse pressure are almostall based on one of only a few methods. Some of the methods described inthe literature include the following measurement of Pulse PressureVariation (PPV), Systolic Pressure Variation (SPV) and Stroke VolumeVariation (SVV).

PPV estimation is based on some version of the following Equation 1:

PPV=100·[PP_(max)−PP_(min))/[½(PP_(max)+PP_(min))]  (Equation 1)

where PP is measured pulse pressure, PP_(max) and PP_(min) are,respectively, the maximum and the minimum peak-to-peak values of thepulse pressure during one respiratory (inspiration-expiration) cycle.

SPV estimation is based on some version of the following Equation 2:

SPV=100·[SP_(max)−SP_(min))/[½(SP_(max)+SP_(min))]  (Equation 2)

where SP is measured systolic pressure, SP_(max) and SP_(min) arerespectively the maximum and minimum values of the systolic pressureduring one respiratory cycle.

Similarly, SVV estimation is based on some version of the followingEquation 3:

SVV=100·[SV_(max)−SV_(min))/[½(SV_(max)+SV_(min))]  (Equation 3)

where SV is stroke volume, SV_(max) and SV_(min) are respectively themaximum and minimum values of the stroke volume during one respiratorycycle.

In Equations 1, 2, and 3, the denominators are the averages of themaximum and minimum values of PP, SP and SV, respectively. In otherwords, the denominators are mean values, albeit of only two measurementpoints. This simple averaging of extreme values has been most commonmerely to simplify the calculations, which have typically been performedby hand. More reliable values may be obtained, however, by using themean of all the measurement values over the measurement interval, thatis, the first statistical moment of PP, SP, and SV.

Thus, for each of PPV, SPV and SVV, the respective variation valueformula expresses the magnitude of the range of the value (maximum minusminimum) relative to the mean of the extreme (maximum and minimum)values.

The specific monitoring of SVV has both specific difficulties andadvantages. Physiologically, SVV is based on several complex mechanismsof cardio-respiratory interaction. In brief: mechanical ventilationcauses changes in left ventricular preload, which leads to distinctvariations in left ventricular stroke volume and systolic arterialpressure. Monitoring of SVV enables prediction of left ventricularresponse to volume administration and helps with correct assessment ofhypovolemia and the subsequent decision to undertake volumeresuscitation in many critical situations.

In addition to the three methods listed above, there is a fourth method,known as Perel's method, which is generally called the “respiratorysystolic variation test.” This method involves airway pressuremaneuvers, such as inducing tidal volumes of varying amplitudes precededby a short apnea period. U.S. Pat. No. 5,769,082 (Perel) describes thismethod. Because of the requirement for pressure maneuvers, this methodis not suitable for real-time monitoring.

The methods listed above are implemented in some CO monitoringinstruments such as LiDCO Ltd.'s cardiac monitor and the PiCCO system ofPulsion Medical Systems (see, for example, U.S. Pat. No.6,315,735—Joeken et al), both of which rely on Equation 3. Tests by theinventors show however, that these methods are so noisy that they do notallow for accurate real-time monitoring of the respiration-inducedchanges in the arterial pulse pressure. The main reason for the noiseproblems in the SVV estimation in those instruments is the way SV iscalculated. For example, the PiCCO system uses a beat-to-beat strokevolume estimation method based on a pulse contour algorithm thatinvolves detection of specific points in the blood pressure waveform,such as the dicrotic notch. Precise detection of the dicrotic notch andother points in the blood pressure signal, however, is difficult, due tothe inconstancy of the blood pressure waveform and its volatile nature.

What is needed is therefore a system and method of operation forestimating SVV in real time more accurately and robustly than is nowpossible, using at most minimally invasive techniques. This inventionmeets this need.

SUMMARY OF THE INVENTION

The invention provides a method and related system implementation fordetermining a cardiac parameter equal to or derivable from cardiacstroke volume variation (SVV): A waveform data set corresponding toarterial blood pressure, determined either invasively or non-invasively,is determined and input to a processing system over a computationinterval that covers at least two cardiac cycles; a standard deviationvalue for the waveform data set is then calculated over each cardiaccycle; and an estimate of the SVV is calculated as a function of thestandard deviation values.

Different methods may be used to calculate the values used in the SVVestimation. For example, maximum and minimum standard deviation valuesover the computation interval may be determined, and the estimate of theSVV can then be calculated as a function of the maximum and minimumstandard deviation values. A mean standard deviation value is preferablyalso computed over the computation interval and the estimate of the SVVcan then be calculated to be proportional to the difference between themaximum and minimum standard deviation values relative to the meanstandard deviation value. As one alternative, the processing system maycompute the standard deviation of the standard deviation values over thecomputation interval and then estimate the SVV as being proportional tothe ratio between the standard deviation of the standard deviationvalues and the mean of the standard deviation values.

Blood pressure may be measured either invasively or non-invasively, forexample by using a catheter-mounted pressure transducer or a fingercuff. The measured arterial pressure is then converted into the waveformdata set.

The inventors have also found that the above-described method accordingto the invention may also be used to calculate an estimate of rightventricular end diastolic volume, which is inversely proportional to thecalculated estimate of the cardiac stroke volume variation.

According to one feature of the invention that has been found to beadvantageous, an approximating function is computed that best matchesthe calculated standard deviation values according to a predeterminedmetric over at least one of the computation intervals. The approximatingfunction is then sampled at an interval-specific sampling rate to createa set of sampled, approximating values, which are then low-pass filteredbefore the estimate of the SVV is computed from them.

This method of approximating, resampling and low-pass filtering with anadjustable rate may be extended for use in estimating other cardiac orhemodynamic parameters than SVV, for example, systolic pressurevariation, pulse pressure variation, etc. In this case, the waveformdata set is generated and input to the processing system to correspondto whatever measurement parameter is selected. A series of measurementvalues is then generated from the waveform data set; an approximatingfunction is computed that best matches the measurement values (or somefunction of them) according to a predetermined metric; over each of atleast one computation interval, a set of sampled, approximating valuesis then created by sampling the approximating function at aninterval-specific sampling rate; the sampled, approximating values arethen low-pass filtered; and an estimate of the output value is thencomputed as a function of the low-pass filtered, sampled approximatingvalues.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustrative example of a complex blood pressure curve overone beat-to-beat heart cycle.

FIG. 2 illustrates a discrete-time representation of the pressurewaveform in FIG. 1.

FIG. 3 illustrates a series of blood pressure signals (waveforms) overdifferent respiratory cycles.

FIG. 4 illustrates beat-to-beat detection in the waveform of FIG. 3,that is, the isolation of individual pressure waveforms per cardiaccycle.

FIG. 5 illustrates a pressure standard deviation curve.

FIG. 6 illustrates optional digital pre-processing involving smoothingand filtering of discrete cardiac or hemodynamic measurement values.

FIG. 7 is a block diagram showing the main components of a systemaccording to the invention.

DETAILED DESCRIPTION Introduction

In broadest terms, the invention involves the beat-to-beat of strokevolume variation SVV as a function of the standard deviation of theblood pressure waveform over a plurality of cardiac cycles. Of course,the invention may be used to determine any other cardiac parameter thatcan be derived from SVV.

The invention may be used to advantage with any type of subject, whetherhuman or animal. Because it is anticipated that the most common use ofthe invention will be on humans in a diagnostic setting, the inventionis described below primarily in use with a “patient.” This is by way ofexample only, however—it is intended that the term “patient” shouldencompass all subjects, both human and animal, regardless of setting.

Because of its clinical significance, it is anticipated that mostimplementations of the invention will generate SVV estimates based onmeasurements of systemic arterial blood pressure. It would also bepossible to use measurements of blood pressure taken elsewhere, however,such as in the pulmonary artery on right side, although such sites mayrequire invasive intracardiac measurement.

Pressure Waveforms

FIG. 1 illustrates an example of a waveform P(t) of arterial pressuretaken over a single heart cycle, here, from the point of diastolicpressure P_(dia) at time t_(dia0), through the time t_(sys) of systolicpressure P_(sys), to a time t_(dial) at which the blood pressure onceagain reaches P_(dia).

According to the invention, P(t), or any signal that is proportional toP(t), may be measured at any point in the arterial tree, eitherinvasively or non-invasively. If invasive instruments are used, inparticular, catheter-mounted pressure transducers, then any artery maybe used as a measurement point. Placement of non-invasive transducerswill typically be dictated by the instruments themselves—the placementof finger cuffs, upper arm pressure cuffs, and earlobe clamps should beobvious. Regardless of the instrument, it will ultimately produce, orcause to be produced, an electric signal corresponding (for example,proportional) to P(t).

Rather than measure arterial blood pressure directly, any other inputsignal may be used that is proportional to blood pressure. Any neededscaling or conversion may then be done at any or all of several pointsin the calculations described below. For example, if some signal otherthan arterial blood pressure itself is used as input, then it may becalibrated to blood pressure before its values are used in thecomputations described below. In short, the fact that the invention mayin some cases use a different input signal than a direct measurement ofarterial blood pressure does not limit its ability to generate anaccurate SVV estimates. The only requirement of this invention is that asignal or data set equal or at least having a known relationship to(such as being proportional to) the patient's blood pressure over theinterval of interest (including continuously) must be made available tothe processing system (see below) that carries out the signalconditioning and various calculations described below.

As is well known, and as is illustrated in FIG. 2, analog signals suchas P(t) can be digitized into a sequence of digital values using anystandard analog-to-digital converter (ADC). In other words, P(t),t0≦t≦tf, can be converted, using known methods and circuitry, into thedigital form P(k), k=0, (n−1), where t0 and tf are initial and finaltimes, respectively, of the computation interval and n is the number ofsamples of P(t) to be included in the calculations, distributed usuallyevenly over the computation interval.

Standard Deviation

The calculation of the mean and standard deviation of a continuous ordiscrete function or data set f is a very well known procedure, and isusually indicated in references by the Greek letters μ and σ,respectively, or, in most programming languages, by function names suchas mean and std. Thus, μ(f) and mean(f) represent the mean of thefunction or data set f over some interval and σ(f) and std(f) representits standard deviation.

Now consider the calculation of the mean and standard deviation of aseries of blood pressure values P=P(k) over some interval such as k=1, .. . , n. The most common way to calculate the mean μ(P) and standarddeviation σ(P) is to use the algorithms familiar to all who have takeneven an introductory course in Statistics:

μ(P)=mean(P)=1/m*SUM[P(k)]  (Equation 4)

σ(P)=std(P)=sqrt{1/(m−1)*SUM[P(i)−μ(P)]²}  (Equation 5)

where sqrt indicates the square root and SUM indicates summation overthe interval i=0, . . . , (m−1). Note that the discrete-value formulasfor variance (the square of standard deviation) usually scale by 1/(m−1)instead of 1/m for well-known statistical reasons.

As will become clearer below, the invention generates a robust estimateof SVV in real time from calculations of the standard deviation of thepressure waveforms, preferably over several cardiac cycles. Although thestandard “textbook” formula for standard deviation (Equation 5) ispreferred for well known statistical reasons, any formula or algorithmthat provides an acceptably accurate value of or corresponding tostandard deviation may be used instead in the invention. For example, atleast in the context of blood pressure-based measurements, a roughapproximation to σ(P) can be had by dividing by three the differencebetween the maximum and minimum measured pressure values. Moreover, themaximum, or absolute value of the minimum, of the first derivative ofthe P(t) with respect to time is generally proportional to σ(P).

In this discussion of the invention are several references tocalculations using “pressure” values and “standard deviation” values. Inthe preferred embodiment of the invention, these are in fact directmeasurements of blood pressure, in particular arterial blood pressure,and standard deviation as computed using the most common formula, givenabove as Equation 5. It is to be understood, however, that “pressure”may equally refer to indirect measurements, or measurements of somephysiological characteristic that correlates or corresponds to or can beotherwise related to pressure. Similarly, “standard deviation” may alsorefer to any value known to approximate the value that would be given bythe usual formula; examples of such alternatives are given in theprevious paragraph.

SVV Computation

The standard formula for calculating cardiac output (CO) is CO=SV·HR,which simply expresses relationship that the amount of blood the heartpumps per minute is equal to how much it pumps per cycle (SV) times thenumber of cycles in a minute. Given HR, the problem, of course, is thatthis assumes a constant value of SV, or knowledge of the mean SV. Basedon the observation that the pulsatility of a pressure waveform iscreated by the cardiac stroke volume into the arterial tree, one of thepresent inventors earlier discovered that SV can be approximated asbeing proportional to the standard deviation of the arterial pressurewaveform P(t), or of some other signal that itself is proportional toP(t). Thus, one way to estimate SV is to apply the relationship

SV=K·σ(P)=K·std(P)  (Equation 6)

where K is a calibration constant and from which follows:

CO=K·σ(P)·HR=K·std(P)·HR  (Equation 7)

Substituting Equation 6 into Equation 3 yields a formula for SVV that isa function of std(P):

SVV=100·[std(P)_(max)−std(P)_(min))]/[½(std(P)_(max)+std(P)_(min))]  (Equation8)

where std(P)_(max) and std(P)_(min) are, respectively, the maximum andminimum values of the standard deviation of the pressure waveform over acomputation interval. In the preferred embodiment of the invention, thiscomputation interval is a respiratory cycle.

As mentioned above, using the statistical mean of pressure—mean(P)—inthe denominator over the measurement interval will generally providemore accurate and robust estimates than using the mean only of themaximum and minimum values, although the invention may use either meanin the denominator. The preferred form of Equation 8 is thus:

SVV=100·[std(P)_(max)−std(P)_(min))]/mean(std(P))  (Equation 9)

where mean(std(P)) is the mean of the standard deviation of the pressurewaveform, not the mean μ(P) of the pressure waveform itself, althoughthis parameter will be included in the calculation of any std(P) value.Also, depending on the type of signal conditioning and conversionmethods (see below) used to condition the measured pressure signal P(t)and then to convert it into discrete form, it may be necessary ordesirable to scale Equation 9. It will be obvious to any skilled systemdesigner whether scaling is needed, and how to do so; for that reason,any scaling factor is not shown in Equation 9 but can be assumed.

FIG. 3 illustrates a sequence of measured or otherwise acquired arterialpressure waveforms over approximately three respiratory cycles. Inpractice, the sequence will be a data set P(k) derived from a sampledmeasurement of arterial pressure P(t). As mentioned above, the P(k)values may be obtained through direct, invasive or non-invasivemeasurement, or may be input from some other source, such as from aremote monitor or even a pre-recorded data set, although this latterpossibility would of course not provide real-time monitoring and wouldin most cases be sued primarily for comparison or experimentation.

In FIG. 4, dots are included in the waveform of FIG. 3 to indicate thebeginning of each cardiac cycle (that is, each “beat”) over theillustrated computation interval. The beginning of each cardiac cyclemay be determined in any of a number of known ways using any knownsystem that is or includes a heart rate monitor. Assuming, for example,as is often the case, that the patients cardiac electrical activity isalso being monitored by an electrocardiogram system (EKG), then thebeginning of each cardiac cycle may be determined to occur at thesampled pressure value immediately following each R-wave.Pressure-based, pulse-rate monitors may also be used and are in factpreferred because they will then be better synchronized with the bloodpressure signal than will, for example, an EKG signal.

If no such external device is present, then the beginning of eachcardiac cycle can also be determined using software alone from thepressure waveform P(k) itself, for example, simply by assuming that eachbeat begins at the time of minimum (diastolic) pressure P_(dia) (seeFIG. 1), or by using Fourier transformation or derivative analysis. Inthese cases, the heart rate “monitor” is a software construct. In suchcase, care should be taken, using known techniques, to ensure that alocal pressure minimum is not caused by respiration itself, but is infact at the diastolic time.

Let P(k,i) be the i′th beat-to-beat arterial pressure signal in acomputation interval. The standard deviation std(P(k,i)) can then becomputed as described above and will be a single-value (scalar) result.The standard deviation values for each of the beat-to-beat arterialpressure signals in the computation interval can be similarly computed.In FIG. 5, each dot on a standard deviation curve std(P(t)) indicatesthe computed standard deviation value for one beat-to-beat arterialpressure signal.

Computation of SVV according to Equation 9 requires the maximum, minimumand mean values of std(P(k,i)) for each computation interval. One way toget std(P)_(max) and std(P)_(min) for a given respiratory cycle (roughlythree respiratory cycles are illustrated in FIG. 5) is simply to takethe greatest and least of the discrete std(P(k,i)) values in the cycle.These can be identified rapidly by simple scanning of the computedvalues.

During actual monitoring, noise and other factors may cause one or morestd(P(k,i)) values to become unreliable. Deviant and potentiallyunreliable std(P(k,i)) values can be detected using known algorithms,such as those based on pattern-matching. Interpolation can then be usedto determine replacements for the excluded value(s). A preferred methodfor smoothing and filtering measured values to increasereliability—applicable even in determinations of other cardiac andhemodynamic parameters than SVV—is described below.

Any standard algorithm may be used to identify std(P)_(max) andstd(P)_(min) from std(P(k,i)). The simplest method is to take thegreatest and least measured values. Alternatively, the measuredstd(P(k,i)) points may be used as the basis for determining anapproximating or smoothing function (for example, using splines orpolynomials); this would in many cases allow for identification ofextreme std(P(t)) values that lie between the computed values, such asstd(P)_(min) shown in FIG. 5. The values mean(std(P(k,i))=mean(std(P))can be calculated using the standard statistical formula (see, Equation4). FIG. 5 also illustrates the value of mean(std(P)) for the firstrespiratory cycle. Once std(P)_(max) and std(P)_(min) are determined fora given respiratory cycle, then an SVV value for that respiratory cyclecan be readily computed according to either Equation 8 or Equation 9.Assuming the preferred case that mean(std(P(k)) is also computed then amore accurate and robust SVV can be computed using Equation 9. Thecomputed value(s) of SVV may then be displayed for the user, stored,transmitted, and/or used in further calculations in any desired way.

As mentioned above, the preferred computation interval is onerespiratory cycle. The beginning and end times of these cycles may bedetected using any known device. Note that many patients who would needthis invention will also be ventilated, in which case the ventilatoritself may provided the needed timing signals for the invention toseparate the different respiratory cycles.

As illustrated in FIGS. 3 and 4, however, it would also be possible todetect the boundaries of respiratory cycles by analyzing the suite ofacquired pressure waveforms itself: The times of the least diastolicpressures (the local minima of the “envelope” of the pressure waveforms)will normally also mark the beginning of a respiratory cycle. In somesituations, however, such a software-based detection method could beless precise than simply receiving a signal from another system thatspecifically includes respiratory monitoring, especially where thepatient's breathing is weak.

Computation Interval—Alternative SVV Computation

Above, it is assumed that an SVV value is estimated for each respiratorycycle. This is not necessary. Rather, it would also be possible to usethe same methodology and equations described above to compute a singleSVV value over a computation interval greater than one respiratorycycle, even over the entire time of a monitoring session. Although thiswould of course not show cycle-to-cycle SVV trends, it may provide moreaccurate results for each monitoring session and thus better indicationof more long-term (such as session-to-session or day-to-day) trends. Itis not necessary always to compute over “extremes” intervals, however.Rather, an SVV value could be computed for any n-cycle time periods,with n ranging from one (the case described above) upward.

Assume, for example, that a computation period is greater than onerespiratory cycle. For the sake of illustration, assume that all threerespiratory cycles shown in FIG. 5 are to constitute a single, combinedcomputation interval. Even in this case, there will be a set std(P(k,i))of computed std(P(k)) values (the “points” on the curve), indeed, evenmore values. These standard deviation values will themselves have astandard deviation and mean (mid-point between extreme values).According to an alternative embodiment of the invention, useful forcomputation intervals spanning more than one respiratory cycle, SVV isestimated thus:

SVV=C·100·std(std(P(k,i))/mean(std(P(k,i))  (Equation 10)

where C is an empirically determined scaling constant. In one test ofthe invention, the inventors determined C to be approximately 2.7,regardless of the number of respiratory cycles included in thecomputation interval; normal experimental methods may be used todetermine C in any given implementation of the invention.

This alternative, multi-cycle method does not require the system todetermine any std(P)_(max) or std(P)_(min) values. Consequently, it isnot even advantageous to determine an interpolating, approximatingfunction for the std(P(k)) values over the computation interval.

Optional Smoothing, Resampling and Filtering

See FIG. 6, in which a sequence of measurement values X(k) of a cardiacor hemodynamic value X is plotted as dots. In the embodiment of theinvention described above, X(k) is std(P(k)), with one measurement valueper cardiac cycle. The optional digital pre-processing described hereis, however, also applicable to any other cardiac or hemodynamic value,such as systolic or pulse pressure, or even a non-pressure relatedparameter such as blood velocity measurements obtained from Dopplerultrasound scanning.

The measurement values will seldom fall neatly on a well-definedprofile, since the underlying parameter is affected not only by noise,but also by natural irregularities such as a non-constant heart rate,different respiration patterns, etc. In many cases, the measurementsystem may itself be able to warn of, identify and exclude unreliablemeasurement values. For example, if signal strength falls below somepredetermined minimum, then the values of the parameter measured duringsuch time may be tagged or excluded. In other cases, unreliable valuesmay be undetectable without further analysis. In FIG. 6, for example,the measurement point marked X(p) deviates so much from the apparentpattern that it could reasonably be assumed to be unreliable.

As mentioned above, one way to identify deviant values is by usingpattern matching, in which the measured points are compared with one ormore pre-stored templates, obtained from controlled studies done for apatient population, or simply verified profiles measured in the samepatient. Any point that deviates from the template(s) by more than somethreshold amount, measured in any known manner, can then be excluded.

In the preferred embodiment of the invention, for each computationinterval, an approximating function (which may be the concatenation orcombination of more than one partial function) is generated so as tocreate an interval profile that best matches the measured pointsaccording to any known metric, that is, in any known sense, such asleast squares. For example, polynomial functions such as splines (twoexamples: B-splines and Bezier curves), reduced-component Fourierrepresentations, etc., may be quickly calculated to generate anappropriate approximating function. In FIG. 6, the approximatingfunction for the first respiratory interval is labeled X*(t).

In the illustrated examples, the computation interval is a respiratorycycle. Other intervals may be chosen depending on the parameter ofinterest, and need not necessarily be related to the respiratory cyclesat all. Even for those that do, it is not necessary for the measurementinterval to be a single cycle, or a whole multiple of single cycles,although this will in general make the most sense where the parameter ofinterest is affected by respiration and will also generally simplifycalculations.

Once the approximating function is computed, the preferred embodiment ofthe invention low-pass filters the values per computation interval. Thetheory and implementation of digital low-pass filters is well known.Some set of sampled values are used as inputs to an algorithm thatcalculates some weighted linear or rational function of them to producea transformed, filtered set of output values. Typical digital filtersgenerally assume a constant “distance” between samples, however, andmost such filters also have fixed coefficients.

According to this aspect of the invention, however, the input values tothe low-pass filter are obtained by sampling the approximatingfunction—possibly (but not necessarily) even at a higher rate than therate at which the actual measurement values were obtained. In FIG. 6,the sample points are indicated by open dots on the approximating curveX*(t). The sample points of the approximating curve X*(t) are then inputto a digital low-pass filter, whose cut-off frequency may be chosen inany known manner, and will depend on the known nature of the hemodynamicor cardiac parameter that is to be estimated, as well as of themeasurement values X(k). Once the desired cut-off frequency isdetermined, then the coefficients of a suitable low-pass filter may bedetermined in any known manner.

Note that this procedure enables even spacing of the sample points, eventhough, because of a changing heart rate, for example, the actualmeasured values may not be evenly spaced. Moreover, note that thesampling rate for respiratory cycle (here chosen as the computationinterval) 3 is greater than that for cycles 1 and 2. One way to selectthe sampling rate for each given computation interval is to choose asmany evenly spaced samples of the approximating curve X*(t) as there areactual measurement values in the computation interval. This is notnecessary, however, but rather the sampling rate may be chosen asdesired, for example, to satisfy the Nyquist criterion and reducealiasing effects for the type of digital low-pass filter used.

Tests by the inventors have shown that these steps of smoothing (via theapproximating function), re-sampling (that is, sampling that occursafter that performed for the analog-to-digital conversion), andadjustable-coefficient low-pass filtering, improve the ability of theinvention to reject noise and produce more reliable SVV values. Asmentioned above, the procedure may also be used for other estimatedparameters than SVV.

System Components

FIG. 7 shows the main components of a system that implements the methoddescribed above for sensing pressure and calculating SVV according tothe invention. The invention may be included within an existingpatient-monitoring device, or it may be implemented as a dedicatedmonitor. As is mentioned above, pressure, or some other input signalproportional to pressure, may be sensed in either or, indeed, both, oftwo ways: invasively and non-invasively. Simply because it isanticipated to be the most common implementation of the invention, thesystem is described as measuring arterial blood pressure as opposed tosome other input signal that is converted to pressure.

FIG. 7 shows both types of pressure sensing for the sake of conciseness;in most practical applications of the invention, either one or severalvariations will typically be implemented. In invasive applications ofthe invention, a conventional pressure sensor 100 is mounted on acatheter 110, which is inserted in an artery 120 of a portion 130 of thebody of a human or animal patient. Such artery could be an ascendingaorta, or pulmonary artery, or, in order to reduce the level ofinvasiveness, the artery 120 could be peripheral, such as the femoral,radial or brachial artery. In the non-invasive applications of theinvention, a conventional pressure sensor 200, such as aphoto-plethysmographic blood pressure probe, is mounted externally inany conventional manner, for example using a cuff around a finger 230 ora transducer mounted on the wrist of the patient. FIG. 3 schematicallyshows both types.

The signals from the sensors 100, 200 are passed via any knownconnectors as inputs to a processing system 300, which includes one ormore processors and other supporting hardware, such as a memory 301, andsystem software (not shown) usually included to process signals andexecute code. The invention may be implemented using a modified,standard, personal computer, or it may be incorporated into a larger,specialized monitoring system. In this invention, the processing system300 also may include, or is connected to, conditioning circuitry 302which performs such normal signal processing tasks as amplification,filtering, ranging, etc., as needed.

The conditioned, sensed input pressure signal P(t) is then converted todigital form by a conventional analog-to-digital converter ADC 304,which has or takes its time reference from a clock circuit 305. As iswell understood, the sampling frequency of the ADC 304 should be chosenwith regard to the Nyquist criterion so as to avoid aliasing of thepressure signal; this procedure is very well known in the art of digitalsignal processing. The output from the ADC 304 will be the discretepressure signal P(k), whose values may be stored in conventional memorycircuitry (not shown).

A signal pre-processing module 306 is preferably included, with routinesto provide such known pre-processing as digital filtering for general(as opposed to interval-to-interval) noise removal, for motion artifactrejection, pulse beat detection (if needed), for rejection of bad beats,etc. This module may also be implemented wholly or partially inhardware. As mentioned above, known circuitry may be included toindicate, for example, that signal strength is too low, and that thedelivered measurement values are unreliable. As such, the module 306 mayalso be located functionally, wholly or partially, before the ADC 304.

The values P(k) are passed (usually, accessed from memory by) to asoftware module 310 comprising computer-executable code for computingthe standard deviation of P(k) over a computation interval such as acardiac cycle, which may be triggered by any known device or softwareroutine 315 that detects heart rate or at least signals the beginning ofa cardiac cycle. Even moderately skilled programmers will know how todesign this software module 310.

Above are described preferred, but optional processing steps ofgenerating an approximating function (see X*(t) in FIG. 6 and therelated discussion), sampling the generated function, and then low-passfiltering the sampled values. Software modules 312, 313, 314 areincluded to perform these functions, and can be programmed using knowtechniques. Of course, any or all of these modules may be combined intoa single body of code; they are shown separately for the sake ofclarity. Also, if the measured or calculated values used as the basisfor the approximating function are not std(P(k)), then the module 310will be replaced, reprogrammed or omitted as needed to provide theappropriate values.

The std(P(k)) values, which will typically be stored in the memory 301,are then passed to a software module 320 that includescomputer-executable code for detecting the maximum, minimum std(P(t))values std(P)_(max) and std(P)_(min) and for computing the meanstd(P(t)) value mean(std(P(k)) for each given computation/measurementinterval, which may be triggered by a respiratory device 325 such as aventilator or detected by a software module as described above. Again,even moderately skilled programmers will know how to design the softwaremodule 320 given the description above. Also as noted above, if thecomputation interval is chosen to extend over more than one respiratorycycle, then it will not be necessary to calculate the maximum andminimum std(P(t)) values std(P)_(max) and std(P)_(min) such that themodule 320 can be omitted or at least not called.

The values std(P)_(max), std(P)_(min) and mean(std(P(k)) are then passedto an SVV calculation module 330, which computes an estimate of SVV forthe chosen interval according to Equation 8 or 9. If a multi-cycleinterval is set, then the SVV calculation module 320 may operatedirectly on the std(P(k)) values provided by module 310 to calculate anestimate of SVV according to Equation 10.

As shown in FIG. 7, any or all of the software modules 306, 310,312-314, 320, and 330 may be implemented simply as routines within asingle estimation software component 370, which may of course becombined with other software components of the processing system 300 asdesired.

The invention further relates to a computer program loadable in acomputer unit or the processing system 300 in order to execute themethod of the invention. Moreover, the various software modules 310,312-314, 315 (if implemented in software), 320, 330, or, in general,370, used to perform the various calculations and perform related methodsteps according to the invention may also be stored ascomputer-executable instructions on a computer-readable medium in orderto allow the invention to be loaded into and executed by differentprocessing systems.

Once an SVV (or other cardiac or hemodynamic) estimate has beencomputed, it is passed to any desired output device 500, such as auser-viewable monitor, and displayed, stored or transmitted in anychosen format. An input device 400 is preferably also included to allowthe user to input, for example, administrative and patient-specificinformation, to adjust the display, to choose the computation interval,etc. Note that if the user is to be allowed to change the computationinterval, then the corresponding information must be made available tothe estimation software component 370 so that it can direct the SVVestimation module to select the required input values when computing SVVaccording to either Equations 8 or 9, or Equation 10.

Test Results

Two different but related methods for computing SVV from std(P(k))values are described above—one in which SVV is calculated for oversingle respiratory cycles and another that may be used to compute asingle SVV value for a computation interval spanning more than onerespiratory cycle. The inventors tested both these embodiments of theinvention on animal femoral and radial blood pressure data. The datawere collected from several pig experiments, which were performed in alaboratory. During the experiments, several changes in the leftventricular volume were induced (such as volume infusions or volumeextractions). Variations of the peripheral resistance (vasodilation orvasoconstriction) were induced as well. Both embodiments of theinvention were found not only to provide similar SVV estimates, but alsothese estimates were found to be superior to those obtained using priorart methods for the sake of comparison.

Additional Outputs

As mentioned above, the invention may be used to estimate not only SVV,but also any cardiac parameter that can be derived from SVV. Theinventors have discovered in tests, for example, that during mechanicalventilation with a constant ventilation rate and a constant tidal volumethe right ventricular end diastolic volume (EDV) is an inverselyproportional to SVV. Thus:

EDV=c/SVV  (Equation 11)

where c is a calibration factor, which may be constant. The SVV estimateprovided by the invention could therefore be used as an indirect methodto estimate EDV, ejection fraction or other values that are known to beproportional to the degree of vascular filling.

The calibration factor c in Equation 11 will depend on severalparameters such as ventricular contractility and ventricular compliance.In general, c will depend on the hemodynamic state of the patient.Recalibration must therefore be performed each time the hemodynamicstatus of the patient changes or during periods of hemodynamicinstability.

1. A method for determining a cardiac or hemodynamic output valuecomprising: inputting a waveform data set corresponding to measurementsof a measurement parameter; generating a series of measurement valuesfrom the waveform data set; computing an approximating function thatbest matches the measurement values according to a predetermined metric;over each of at least one computation interval, creating a set ofsampled, approximating values by sampling the approximating function atan interval-specific sampling rate; low-pass filtering the sampled,approximating values; and calculating an estimate of the output value asa function of the low-pass filtered, sampled approximating values.
 2. Amethod as in claim 1, in which the output value displaysrespiration-induced variation, further comprising: identifyingrespiratory cycles; detecting cardiac cycles; setting the computationinterval to be a respiratory cycle; and for each computation interval,setting the interval-specific sampling rate as a function of the numberof cardiac cycles in each respective respiratory cycle.
 3. A method asin claim 1, in which the step of generating the series of measurementvalues includes pre-processing the waveform data set.
 4. A method as inclaim 1, in which the waveform data set corresponds to blood pressure,further comprising computing each measurement value to be a function ofthe standard deviation of blood pressure over each respectivecomputation interval.
 5. A method as in claim 1, in which the outputvalue is systolic pressure variation.
 6. A method as in claim 1, inwhich the output value is pulse pressure variation.
 7. A system fordetermining a cardiac or hemodynamic output value comprising: anarrangement for determining and inputting a waveform data setcorresponding to measurements of a measurement parameter; a low-passfilter; a processing system including computer-executable code forgenerating a series of measurement values from the waveform data set;for computing an approximating function that best matches themeasurement values according to a predetermined metric; over each of atleast one computation interval, for creating a set of sampled,approximating values by sampling the approximating function at aninterval-specific sampling rate; calculating an estimate of the outputvalue as a function of the sampled approximating values after filteringby the low-pass filter.
 8. A system as in claim 7, in which the outputvalue displays respiration-induced variation, further comprising: anarrangement for identifying respiratory cycles; an arrangement fordetecting cardiac cycles; in which the processing system furtherincludes additional computer-executable code for setting the computationinterval to be a respiratory cycle; and for each computation interval,setting the interval-specific sampling rate as a function of the numberof cardiac cycles in each respective respiratory cycle.
 9. A system asin claim 7, further including a pre-processing module, included in theprocessing system, that pre-processes the series of measurement valuesincludes pre-processing the waveform data set.
 10. A system as in claim7, in which the arrangement for determining and inputting the waveformdata includes a mechanism for determining blood pressure, the waveformdata set corresponds to blood pressure, in which the processing systemfurther includes additional computer-executable code for computing eachmeasurement value to be a function of the standard deviation of bloodpressure over each respective computation interval.
 11. A system as inclaim 7, in which the output value is systolic pressure variation.